Submitted by Group 25:
Upload: 08.11.2023 (11:30)
Deadline: 21.11.2023 (23:59)
Please hand in a single .zip file named according to the pattern "groupXX_exerciseX" (e.g. group00_exercise9). The contents of the .zip should be as follows:
I.e.
Given a camera with a distance $L$ between the film and the lens, derive the mathematical relationship (formula) between the height $H_o$ of the object in front of the camera and the height $H_i$ of its image. Additionally, explain the intuition behind the relationship. Assume a thin lens.
An Object is roated around the x-axis by $90°$, then around the y-axis by $270°$, and finally around the z-axis by $180°$.
Derive the 3D Roation Matrix that executes the same transformation.
Hint: the given values lead to 'nice' numbers.
Assume the object is a sphere with a radius of 3.5. Explain how the radius will change after the transformation.
No, the radius of the sphere does not change after transformation. It remains 3.5
What is the rotation matrix that transforms the object back to its original orientation?
Hint: this should be very short
It will be the transpose of the rotation matrix.
Why are homogeneous coordinates used for transforming points between coordinate systems?
Homogeneous coordinates are used for transforming points between coordinate systems because they make all the transformations linear which can be represented by a single matrix.
Describe the transformation chain for mapping a point from the world coordinate system to the pixel coordinate system of an intrinsically and extrinsically calibrated camera. Use formulas and explain the intermediate steps in words.
Describe the steps for modelling distortion.